We have a tool that that will generate flat turn radii but do we have a tool that will for a particular speed give you the vert turn radius? Also, if maybe one could dial in a direction vector and an up vector, (or a quaternion), and it would calculate the turn radius for that position given a speed. Does such tool exist?
Yes such tools exist. It's called a simulator! I'm being very serious of course.
What you're asking for is something to model the interactions in a SUSTAINED vertical turn so that you can predict the performance of an airplane. Even assuming we're talking about a perfect loop meaning no oblique angles involved (lift vector 100% in the plane of the weight vector all through the maneuver) it requires many iterative calculations to solve because key variables are dynamic and changing. In other words your solving differential equations.
In a SUSTAINED LEVEL TURN we don't have to worry about all this and can simplify this because we can assume key variables are fixed/constant, particularly constant velocity, constant g-load, constant lift and weight vector orientation to one another, etc which leads us to use usual level turn radius and turn rate equations not involving nasty PDE's. We don't have these luxuries for sustained vertical turns so there's no easy way to plug a flight test data points into a spreadsheet and crank out a turn rate and radius projections that would be meaningful.
Sure, you could try to simplify it (e.g. plug in 4 sets of data points for instance) but I have no clue how that would be useful or how you could make any meaningful projections from such a procedure.
In short to get the same fidelity in turn rate and turn radius projections that we have for sustained level turns, you have to use numerical methods of solving differential equations to do so which means creating a simulator essentially.
Tango
412th FS Braunco Mustangs
